Final answer:
To find the value of n in the arithmetic sequence, David used the explicit formula and solved for n when the nth term of the sequence was given as 73.
Step-by-step explanation:
To find the explicit formula for the arithmetic sequence with the first term of 1013 and a common difference of 1619, we can use the formula:
sn = a + (n-1)d
where sn represents the nth term of the sequence, a is the first term, n represents the number of terms, and d is the common difference.
In this case, we want to find the value of n when the nth term of the sequence is 73. Substituting the given values into the formula, we get:
73 = 1013 + (n-1)1619
Next, we simplify the equation:
73 = 1013 + 1619n - 1619
Combine like terms:
73 = 1619n - 606
Move the constant to the other side:
1619n = 73 + 606
1619n = 679
Divide both sides by 1619:
n = 679 ÷ 1619
n ≈ 0.4198
Therefore, the value of n that David used is approximately 0.4198.